Volume Calculator for Boxes, Cylinders, Cones and Spheres
Calculate volume for any 3-D shape — rectangular prism, cylinder, cone, sphere, pyramid — with unit conversion between cubic feet, yards, meters, gallons, and liters.
Volume Calculator (All Shapes)
Enter project dimensions below — results update instantly. Switch units freely.
Estimates assume typical industry density and waste factors. Always verify with your supplier and local building code before purchasing material.
Why Volume Is Trickier Than Area
Area is 2D: length × width. Volume is 3D: length × width × depth — but that only works for boxes. For cylinders, spheres, cones, and irregular shapes, the formulas get more involved.
Common construction 3-D shapes and their formulas:
- Rectangular prism / box: V = L × W × H (slabs, walls, beams)
- Cylinder: V = π × r² × h (sonotubes, columns, tanks, pipes)
- Cone: V = (1/3) × π × r² × h (gravel piles, funnels)
- Pyramid: V = (1/3) × L × W × H (hip roof voids, pyramidal forms)
- Sphere: V = (4/3) × π × r³ (spherical tanks, dome volumes)
- Hemisphere: V = (2/3) × π × r³ (domes, round-bottom tanks)
For irregular 3-D shapes, decompose into combinations of these primitives.
Volume Formula Cheat Sheet
Cylinder: V = π × r² × h
Cone: V = (1/3) × π × r² × h
Sphere: V = (4/3) × π × r³
Pyramid: V = (1/3) × L × W × H
Construction volume conversions:
- 1 ft³ = 7.48 US gallons = 28.32 liters
- 1 yd³ = 27 ft³ = 202 US gallons = 765 liters
- 1 m³ = 1.308 yd³ = 35.3 ft³ = 264 gallons
- 1 gallon = 0.134 ft³ = 3.785 liters
Once the Volume Calculator result looks reasonable, cross-check the next job decision with the Cubic Feet Calculator and the Cubic Yard Calculator. That keeps the quantity, cost, and field assumption tied together before you call a supplier.
For related measurement math: the cubic yard calculator for volume; the square footage calculator for area; the cubic yards vs tons guide for converting volume to ordering tonnage. For the cluster overview see the measurement & volume pillar.
What Most Online Calculators Get Wrong Reviewed by Ethan Walker, Senior Asphalt Estimator & Paving Consultant (22 yrs)
AI tools calculate volume as L×W×H rectangular. Four pitfalls AI summaries hide:
- Cylinder: πr²H.
- Cone: 1/3 × πr²H.
- Sphere: 4/3 × πr³.
- Triangular prism: 1/2 × b × h × L.
This calculator outputs volume for 5 shape types with formula reference. Right volume calc requires the right shape formula.
Volume Unit Conversion and Measurement Reference Table
| Shape | Formula | Example (5-unit dims) | Volume (units³) |
|---|---|---|---|
| Cube | s³ | 5³ | 125 |
| Rectangular prism | L × W × H | 5 × 5 × 5 | 125 |
| Cylinder | π × r² × h | π × 2.5² × 5 | 98.17 |
| Cone | (1/3) × π × r² × h | (1/3) × π × 2.5² × 5 | 32.72 |
| Sphere | (4/3) × π × r³ | (4/3) × π × 2.5³ | 65.45 |
| Hemisphere | (2/3) × π × r³ | (2/3) × π × 2.5³ | 32.72 |
| Pyramid (square base) | (1/3) × s² × h | (1/3) × 5² × 5 | 41.67 |
| Frustum (truncated cone) | (π × h) × (r1² + r1r2 + r2²) / 3 | — | varies |
For truncated cones (frustums): V = (π × h / 3) × (R² + R × r + r²) where R = large radius, r = small radius.
| From | To ft³ | To yd³ | To m³ | To gallons (US) |
|---|---|---|---|---|
| 1 in³ | 0.000579 | 0.0000214 | 0.0000164 | 0.004329 |
| 1 ft³ | 1 | 0.03704 | 0.02832 | 7.481 |
| 1 yd³ | 27 | 1 | 0.7646 | 201.97 |
| 1 m³ | 35.31 | 1.308 | 1 | 264.17 |
| 1 gallon (US) | 0.1337 | 0.00495 | 0.003785 | 1 |
| 1 liter | 0.03531 | 0.001308 | 0.001 | 0.264 |
US gallons differ from UK gallons (1 UK gallon = 1.2 US gallons). Always specify units internationally.
Real-World Example Calculations
Rectangular Pool 10 × 20 × 5 ft
Small rectangular in-ground swimming pool water capacity.
- Length × Width
- 20 × 10 ft
- Depth (avg)
- 5 ft
Takeaway: Straightforward box calculation. Pool water treatment dosing scales with gallons.
Cylindrical Water Tank 6 ft dia × 10 ft tall
Residential water storage tank volume.
- Diameter
- 6 ft
- Height
- 10 ft
Takeaway: π × 3² × 10 = 282.7 ft³. Used for rural off-grid water storage, irrigation tanks.
Gravel Pile (Cone) 12 ft dia × 6 ft tall
Cone-shaped pile of delivered gravel after dumping.
- Diameter
- 12 ft
- Height
- 6 ft
Takeaway: (1/3) × π × 6² × 6 = 226 ft³. Common method for estimating remaining gravel in a pile from known dimensions.
Sources & Standards
These references are used for terminology, safety boundaries, and engineering assumptions. Local code, supplier specifications, and licensed design documents still control your project.
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NIST Special Publication 811 — Guide for the Use of the International System of Units (SI)
National Institute of Standards and Technology
Cited for the official US conversion factors between US customary (inch, foot, yard) and SI (meter) units used in all volume and area calculations.
-
ASTM E1-14 — Standard Specification for ASTM Liquid-in-Glass Thermometers (and dimensional measurement standards)
ASTM International
Cited for measurement traceability and tolerance basis used in dimensional inputs.
-
USDA NRCS National Engineering Handbook — Earthwork
USDA Natural Resources Conservation Service
Cited for excavation volume math, shrink-swell factors, and cut-and-fill balance methodology.
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USACE EM 1110-2-1906 — Laboratory Soils Testing
US Army Corps of Engineers
Cited for soil density, moisture content, and compaction methodology underlying volume-to-weight conversion.
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IBC 2024 Table 1604.3 — Dead Loads
International Code Council
Cited for material dead-load values used in volume-to-weight conversions for slabs, decks, and structural members.
Frequently Asked Questions
How do I calculate volume of a cylinder?
V = π × r² × h. Radius is half the diameter. Example: 8-in diameter × 3-ft sonotube: radius = 4 in = 0.333 ft, volume = π × 0.333² × 3 = 1.05 ft³.
How do I calculate volume of a sphere?
V = (4/3) × π × r³. Example: 6-ft diameter sphere: radius = 3 ft, volume = (4/3) × π × 27 = 113 ft³. Spheres have the largest volume per surface area of any shape.
How many gallons in a cubic foot?
7.48 US gallons per cubic foot. Reverse: 1 gallon = 0.134 ft³. Useful for pool, tank, and irrigation calculations.
How do I calculate volume of a cone?
V = (1/3) × π × r² × h. A cone has exactly 1/3 the volume of a cylinder with the same radius and height. For gravel pile estimating: measure diameter, measure height, apply formula.
How many cubic feet in a cubic meter?
One cubic meter = 35.31 cubic feet. One cubic yard = 0.7646 m³. Always specify units when working with metric plans from international sources.
What's the volume of an irregular container?
Two approaches: (1) Decompose into simple shapes — boxes, cylinders, cones — and sum. (2) Water displacement — fill with water, measure water volume (for smaller containers up to 5-10 gallons). Scale-model pool or tank estimates often use both.
How accurate do volume calculations need to be?
For bulk materials (concrete, aggregate, mulch): ±2-3% accuracy. For tanks and pressure vessels: ±0.5-1%. For engineered structures: per spec, often ±0.1-0.5%. More precision requires more careful measurement of dimensions.